Solve for $x$ and $y$ using elimination. ${-3x-2y = -20}$ ${5x+2y = 24}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $2x = 4$ $\dfrac{2x}{{2}} = \dfrac{4}{{2}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-3x-2y = -20}\thinspace$ to find $y$ ${-3}{(2)}{ - 2y = -20}$ $-6-2y = -20$ $-6{+6} - 2y = -20{+6}$ $-2y = -14$ $\dfrac{-2y}{{-2}} = \dfrac{-14}{{-2}}$ ${y = 7}$ You can also plug ${x = 2}$ into $\thinspace {5x+2y = 24}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + 2y = 24}$ ${y = 7}$